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Let me tell you, that the board exam marks are not significant for admission unless you're the university topper. Applying for NITs, IITs, IIITs and GFTIs, requires you to be in the Top 20 percentile in your respective board(which you are). But with your JEE score I think you haven't cleared JEE mains, so you won't get these government colleges. So if you want to apply, you can, and keep your hopes, and don't miss the opportunity if it knocks. All the best!
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